Whatever happened to 10 and 16 gauge shotguns? Excerpt:
The 16-gauge enjoyed popularity into the early 20th century, perhaps not coincidentally in conjunction with the golden age of American shotgun manufacture.
Manufacturers such as L.C. Smith, Parker, Ithaca, A.H. Fox and others crafted beautiful 16-gauge side-by-sides. They were sleek, balanced and — at little more than six pounds — they were well-suited for lengthy carry and the snap-style shooting required of grouse, woodcock and quail. Magazine-operated pump-actions also came into fashion, most notably the Remington Model 31, Winchester Model 12 and bottom-ejection Ithaca Model 37. The 16-gauge was long considered more sporting than the 12-gauge, a tool at that time of market gunning and deer hunting.
And on the 10 gauge:
For much of the 19th century, the 10-gauge side-by-side was considered a fine all-around shotgun. Typical loads consisted of 1¼-ounces of shot — a far cry from today’s 2-ounce payloads — and shells were 2-7/8 inches, not 3-½-inch magnums. Period 10-gauges also weighed 8 to 9-½ pounds, much lighter than today’s 10-pound guns. They were suitable for carry by upland hunters, deer hunters and even security guards defending Wells Fargo stage coaches. However, by 1900, the lighter 12-gauge had cemented its role as the every-purpose shotgun, and the 10-gauge was typecast as a niche, waterfowler’s gun.
I’ve never owned a 10 gauge, and such newer 10 gauge guns that are available tend to be long, heavy waterfowling pieces. There’s a good reason for that; the big 2-ounce shot charge thrown by the 3 1/2″ 10 gauge shell was perfect for big, tough Canada honkers.
In the considered opinion of yr.obdt., the main thing involved in the loss of 10 and 16 gauge popularity is ammunition. When the Old 
Man bought his Stevens pump in 1946, only 2 3/4″ 12 gauge loads were available. That was plenty for the pheasants, rabbits and ducks he shot on the farm, and 2 3/4″ slugs would put down a big farm-country whitetail with ease.
But hardened waterfowlers still had reason to favor the big, heavy 10, and upland bird hunters who may walk miles behind a brace of pointers in a day might favor the 16. But improved 20-gauge loads made light shotguns more versatile, and the 3″ 12 gauge – and later, the big 3 1/2″ 12 gauge Roman candles – made the 12 able to encroach into what was traditionally 10 gauge territory.
But the big fringe benefit of the declining popularity of the sweet 16? Vintage shotguns in that age are declining in price. 16 gauge Model 12s are easily available for under five bills, although the Browning Sweet 16 is still pricey. It’s something of a boon to collectors.
